|Date of birth||30 July 1987|
|Place of birth||Mostar, SFR Yugoslavia|
|Height||1.92 m (6 ft 3 1⁄2 in)|
|–2004||Red Star Belgrade|
|2011–2013||Paços de Ferreira||6||(0)|
|* Senior club appearances and goals counted for the domestic league only|
Kojić started playing football at Red Star Belgrade where he spent the majority of his youth career. At 17, Kojić moved to FK Dinamo Pančevo that at the time played in Serbian 3rd division. Starting to play for a senior team when he was only 17 years old turned out to be a good move. He played in 16 games and conceded only 6 goals. At the age of 18 he moved to FK Obilić playing back then in the First League of Serbia and Montenegro. At the end of the season he moved to FK Rad where he played throughout the first part of the season. At the age of 20 he moved to FK Hajduk Beograd where he played 28 games and in April 2009 he signed a contract for Dinamo București. During the winter break of the 2010-11 season, he signed a contract for Cypriot First Division club Doxa Katokopias.
Playing for Hajduk Beograd during 2008-09, Kojić advanced to the last 16 in the Serbian Cup. In the round of 16, Hajduk played FK Vojvodina, which was at the time ranked 2nd in the Serbian Premier League, and knocked them out reaching the last 8 in the National Cup which records for the best result in team's history. In this historic game, Igor not only had a great overall game but he saved 4 penalty kicks and scored the winning goal in the penalty shootout thus setting a unique European record as the only goalkeeper who saved 4 penalties in one game and later on scored the winning goal.
- Kojic sign for Doxa Katokopias at kurir-info.rs (in Serbian)
- "Top 5 goalkeepers who saved 3 penalties in 1 game". footballburp.com. 2015-10-07. Retrieved 2019-03-04.